2003 ks3 maths - paper 2 - level 6-8

7/24/2019 2003 KS3 Maths - Paper 2 - Level 6-8

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Mathematics test

Paper 2Calculator allowed

Please read this page, but do not open your booklet until your

teacher tells you to start. Write your name and the name of

your school in the spaces below.

First name

Last name

School

Remember

The test is 1 hour long. You may use a calculator for any question in this test.

You will need: pen, pencil, rubber, ruler and a scientific orgraphic calculator.

Some formulae you might need are on page 2.

This test starts with easier questions.

Try to answer all the questions.

Write all your answers and working on the test paper

do not use any rough paper. Marks may be awardedfor working.

Check your work carefully.

Ask your teacher if you are not sure what to do.

2003

3

KEY STAGE

68TIER

Ma

For markers

use only

Total marks

Borderline check

QCA/03/971

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KS3/03/Ma/Tier 68/P22

FormulaeYou might need to use these formulae

Volume = area of cross-section t length

Prism

Trapezium

Area = (a +b)h1

2

Instructions

Answers

This means write down your

answer or show your working

and write down your answer.

Calculators

You may use a calculator to

answer any question in this test.

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Ratio of ages

1. Paul is 14 years old.

His sister is exactly 6 years younger, so this year she is 8 years old.

This year, the ratio of Pauls age to his sisters age is 14 : 8

14 : 8 written as simply as possible is 7 : 4

(a) When Paul is 21, what will be the ratio of Pauls age to his sisters age?

Write the ratio as simply as possible.

:

(b) When his sister is 36, what will be the ratio of Pauls age to his sisters age?

Write the ratio as simply as possible.

:

(c) Could the ratio of their ages ever be 7 : 7?

Tick () Yes or No.

Yes No

Explain how you know.

1 mark

1 mark

1 mark

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Nets

3. The squared paper shows the nets of cuboid A and cuboid B.

(a) Do the cuboids have the same surface area?

Show calculations to explain how you know.

(b) Do the cuboids have the same volume?

Show calculations to explain how you know.

1 mark

2 marks

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(b) The data for the beach that had been cleaned represent 15 animals.

Complete the table to show how many of each animal were found on the

cleaned beach.

(c) Cleaning the beach changes the numbers of animals and

the proportions of animals.

Write a sentence to describe both these changes.

2 marks

1 mark

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Equations

5. Find the values of tandr

=

t=

=

r=

5r

2

3

t

6

2

3

1 mark

1 mark

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Star design

6. This pattern has rotation symmetry of order 6

(a) What is the size of angle w ?

Show your working.

(b) Each quadrilateral in the pattern is made from

two congruent isosceles triangles.

What is the size of angle y?

Show your working.

Not drawnaccurately

Not drawn

accurately

2 marks

2 marks

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Ks and ms

7. On the square grids below you can join dots with two different length lines.

Length m is greater than length k

(a) Draw a shape with each perimeter shown below.

The first one is done for you.

Perimeter 4k+ 3m

Perimeter 4k+ m

Perimeter 2 ( 2k+ m )

1 mark

1 mark

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(b) What is the area of this triangle?

Write it in terms of m

(c) This is the same triangle and grid.

What is the area of the triangle?

Write it in terms of k

(d) Using your answers to (b) and (c), explain why m2 = 2k2

1 mark

1 mark

1 mark

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Giraffe

8. A book gives this information:

Suppose the baby giraffe continued to grow at this rate.

About how many days old would it be when it was 6 metres high?

Show your working.

days old

A baby giraffe was born that was 1.58 metres high.

It grew at a rate of 1.3 centimetres every hour.

3 marks

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Long-eared owls

9. Owls eat small mammals.

They regurgitate the bones and fur in balls called pellets.

The table shows the contents of 62 pellets from long-eared owls.

(a) Show that the total number of mammals found is 170

(b) Calculate the mean number of mammals found in each pellet.

Show your working and give your answer correct to 1 decimal place.

(c) There are about 10000 long-eared owls in Britain.

On average, a long-eared owl regurgitates 1.4 pellets per day.

Altogether, how manymammals

do the 10000 long-eared owls eatin one day?

Show your working and give your answer to the nearest thousand.

1 2 3 4 5 6

Frequency 9 17 24 6 5 1

Number of mammalsfound in the pellet

1 mark

2 marks

2 marks

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Pictures

10. Here are four pictures, A, B, C and D. They are not to scale.

(a) Picture A can be stretched horizontally to make picture B.

Show that the horizontal factor of enlargement is 1.5

(b) Picture A can be stretched vertically to make picture C.

The vertical factor of enlargement is 1.25

What is the height, h, of picture C?

cm

1 mark

1 mark

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(c) Show that pictures A and D are not mathematically similar.

(d) Picture E (not shown) is mathematically similar to picture A.

The width of picture E is 3cm.

What is the height of picture E?

cm

1 mark

1 mark

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Coffee

11. A cup of coffee costs 1.75

The diagram shows how much money different people get when you buy

a cup of coffee.

(a) Complete the table to show what percentage of the cost of a cup of coffee

goes to retailers, growers and others.

Show your working.

Retailers %

Growers %

Others %

Not drawnaccurately

2 marks

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(b) Some people think the growers should get more.

Suppose the percentages changed to:

Suppose the retailers still got 44p from each cup of coffee sold.

How much would a cup of coffee cost?

Show your working.

Retailers 23%

Growers 10%

Others 67%

2 marks

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Cissoid of Diocles

12. The equation of the curve shown is

Whenx = 2.5 calculate the positive value of y

Show all the digits on your calculator display.

Whenx = 2.5 give both values of y correct to 3 significant figures.

and

1 mark

2 marks

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Populations

13. The table shows information about some countries.

(a) Use the table to fill in the gaps:

The country with the largest population is

The country with the smallest area is

(b) On average, how many more people per km2 are there in the

United Kingdom than in the United States?

Show your working.

Country Population Area (km2)

Canada 3.1 t 107 1.0 t 107

France 6.0 t 107 5.5 t 105

Gambia 1.4 t 106 1.1 t 104

India 1.0 t 109 3.3 t 106

United Kingdom 6.0 t 107 2.4 t 105

United States 2.8 t 108 9.3 t 106

3 marks

1 mark

1 mark

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Joining

14. Tworight-angled triangles are joined together to make

a larger triangle ACD.

(a) Show that the perimeter of triangle ACD is 78cm.

(b) Show that triangle ACD is also a right-angled triangle.

Not drawnaccurately

2 marks

2 marks

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Squares X

15. y2 represents a square number; y is an integer.

(a) Think about the expression 9 +y2

Explain how you know there are values of y for which this expressiondoes not represent a square number.

(b) Explain why the expression 16y2 must represent a square number.

1 mark

1 mark

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Cylinder

16. A cylinder has a radius of2.5cm.

The volume of the cylinder, in cm3, is 4.5

What is the height of the cylinder?

Show your working.

cm3 marks

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Triangle

17. The diagram shows a triangle.

Side XY is of length 11b

Side XZ is of length 2a + 3b

Side YZ is of length a

The triangle is isosceles, with XY = XZ

The perimeter of the triangle is 91

Use algebra to find the values of a andb

a = b =

1 mark

1 mark

1 mark

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END OF TEST

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2003 ks3 maths - paper 2 - level 6-8

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